Evolution of imitation networks in Minority Game model |
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Authors: | H Lavička F Slanina |
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Institution: | (1) Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 11519, Prague 1, Czech Republic;(2) Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague, Czech Republic and Center for Theoretical Study, Jilská 1, Prague, Czech Republic |
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Abstract: | The Minority Game is adapted to study the “imitation dilemma”,
i.e. the tradeoff between local benefit and global harm coming from
imitation. The agents are placed on a substrate network and are
allowed to imitate more successful neighbours. Imitation domains, which are
oriented trees, are formed. We investigate size distribution of the
domains and in-degree distribution within the trees. We use four types of
substrate: one-dimensional chain; Erd?s-Rényi graph;
Barabási-Albert scale-free graph; Barabási-Albert 'model A'
graph. The behaviour of some features of the imitation network strongly
depend on the information cost epsilon,
which is the percentage of gain the
imitators must pay to the imitated. Generally, the system tends to
form a few domains of equal size. However, positive epsilon makes
the system stay in a long-lasting metastable state with complex
structure. The in-degree distribution is found to follow a power law
in two cases of those studied: for Erd?s-Rényi substrate for any
epsilon and for Barabási-Albert scale-free substrate for large
enough epsilon. A brief comparison with empirical data is provided. |
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Keywords: | 89 65 -s Social and economic systems 05 40 -a Fluctuation phenomena random processes noise and Brownian motion 02 50 -r Probability theory stochastic processes and statistics |
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